What is the sum of the interior angles of a dodecagon?

Understand the Problem

The question is asking for the calculation of the sum of the interior angles of a dodecagon, which is a twelve-sided polygon. The sum can be calculated using the formula (n - 2) * 180, where n is the number of sides.

Answer

The sum of the interior angles of a dodecagon is $1800$ degrees.

Steps to Solve

Identify the number of sides First, we note that a dodecagon has $n = 12$ sides.
Apply the formula for the sum of interior angles We can use the formula for the sum of the interior angles of a polygon, which is

$$ \text{Sum of interior angles} = (n - 2) \times 180 $$

Now substituting the value of $n$:

$$ \text{Sum of interior angles} = (12 - 2) \times 180 $$

Calculate the result Now, perform the calculations:

$$ \text{Sum of interior angles} = 10 \times 180 = 1800 $$

Thus, the sum of the interior angles of a dodecagon is $1800$ degrees.

The sum of the interior angles of a dodecagon is $1800$ degrees.

More Information

A dodecagon is a polygon with twelve sides, and the sum of its interior angles can be calculated using the general formula for any polygon. This method is a fundamental concept in geometry that helps in understanding the properties of polygons.

Tips

Miscounting the number of sides of the polygon can lead to incorrect results. Always ensure to count the sides correctly.
Forgetting to subtract 2 from the number of sides before multiplying can also cause misunderstandings.

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